SOLUTION: What is the sum of the first 500 counting numbers? i.e., The sum of 1+2+3+4...496+497+498+499+500? How about only the odd numbers?

Algebra ->  Human-and-algebraic-language -> SOLUTION: What is the sum of the first 500 counting numbers? i.e., The sum of 1+2+3+4...496+497+498+499+500? How about only the odd numbers?      Log On


   

Question 485643: What is the sum of the first 500 counting numbers? i.e., The sum of 1+2+3+4...496+497+498+499+500? How about only the odd numbers?
Found 2 solutions by richard1234, MathLover1:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of first 500 counting numbers = 500(501)/2 = 125250.

Sum of first 500 odd positive numbers = 500^2 = 250000.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
add first and last
1+=+500+=+501
Do the same with the second highest and the second smallest.
2+%2B+499+=+501
As you can see, all the totals equal 501. Now just divide 500 by 2 since you are using two unique numbers per combination.
500%2F2+=+250
So, the average is %281%2B500%29%2F2+and there are 500 number is the list, so the sum is:
%28501%2F2%29500+=+250%2A501=125250